internal static BigInteger consBigInteger(int bitLength, int certainty, Random rnd)
{
// PRE: bitLength >= 2;
// For small numbers get a random prime from the prime table
if (bitLength <= 10) {
int[] rp = offsetPrimes[bitLength];
return BIprimes[rp[0] + rnd.Next(rp[1])];
}
int shiftCount = (-bitLength) & 31;
int last = (bitLength + 31) >> 5;
BigInteger n = new BigInteger(1, last, new int[last]);
last--;
do {// To fill the array with random integers
for (int i = 0; i < n.numberLength; i++) {
n.digits[i] = rnd.Next();
}
// To fix to the correct bitLength
n.digits[last] = (int)((uint)n.digits[last] | 0x80000000);
n.digits[last] = (int)(((uint)n.digits[last]) >> shiftCount);
// To create an odd number
n.digits[0] |= 1;
} while (!isProbablePrime(n, certainty));
return n;
}
internal static BigInteger and(BigInteger val, BigInteger that)
{
if (that.sign == 0 || val.sign == 0) {
return BigInteger.ZERO;
}
if (that.Equals(BigInteger.MINUS_ONE)){
return val;
}
if (val.Equals(BigInteger.MINUS_ONE)) {
return that;
}
if (val.sign > 0) {
if (that.sign > 0) {
return andPositive(val, that);
} else {
return andDiffSigns(val, that);
}
} else {
if (that.sign > 0) {
return andDiffSigns(that, val);
} else if (val.numberLength > that.numberLength) {
return andNegative(val, that);
} else {
return andNegative(that, val);
}
}
}
internal static BigInteger andDiffSigns(BigInteger positive, BigInteger negative)
{
int iPos = positive.getFirstNonzeroDigit();
int iNeg = negative.getFirstNonzeroDigit();
// Look if the trailing zeros of the negative will "blank" all
// the positive digits
if (iNeg >= positive.numberLength) {
return BigInteger.ZERO;
}
int resLength = positive.numberLength;
int[] resDigits = new int[resLength];
// Must start from max(iPos, iNeg)
int i = Math.Max(iPos, iNeg);
if (i == iNeg) {
resDigits[i] = -negative.digits[i] & positive.digits[i];
i++;
}
int limit = Math.Min(negative.numberLength, positive.numberLength);
for ( ; i < limit; i++) {
resDigits[i] = ~negative.digits[i] & positive.digits[i];
}
// if the negative was shorter must copy the remaining digits
// from positive
if (i >= negative.numberLength) {
for ( ; i < positive.numberLength; i++) {
resDigits[i] = positive.digits[i];
}
} // else positive ended and must "copy" virtual 0's, do nothing then
BigInteger result = new BigInteger(1, resLength, resDigits);
result.cutOffLeadingZeroes();
return result;
}
internal static bool isProbablePrime(BigInteger n, int certainty)
{
// PRE: n >= 0;
if ((certainty <= 0) || ((n.numberLength == 1) && (n.digits[0] == 2))) {
return true;
}
// To discard all even numbers
if (!n.testBit(0)) {
return false;
}
// To check if 'n' exists in the table (it fit in 10 bits)
if ((n.numberLength == 1) && ((n.digits[0] & 0XFFFFFC00) == 0)) {
return (Array.BinarySearch(primes, n.digits[0]) >= 0);
}
// To check if 'n' is divisible by some prime of the table
for (int i = 1; i < primes.Length; i++) {
if (Division.remainderArrayByInt(n.digits, n.numberLength,
primes[i]) == 0) {
return false;
}
}
// To set the number of iterations necessary for Miller-Rabin test
int ix;
int bitLength = n.bitLength();
for (ix = 2; bitLength < BITS[ix]; ix++) {
;
}
certainty = Math.Min(ix, 1 + ((certainty - 1) >> 1));
return millerRabin(n, certainty);
}
public static BigInteger karatsuba(BigInteger op1, BigInteger op2)
{
BigInteger temp;
if (op2.numberLength > op1.numberLength) {
temp = op1;
op1 = op2;
op2 = temp;
}
if (op2.numberLength < whenUseKaratsuba) {
return multiplyPAP(op1, op2);
}
/* Karatsuba: u = u1*B + u0
* v = v1*B + v0
* u*v = (u1*v1)*B^2 + ((u1-u0)*(v0-v1) + u1*v1 + u0*v0)*B + u0*v0
*/
// ndiv2 = (op1.numberLength / 2) * 32
int ndiv2 = (int)(op1.numberLength & 0xFFFFFFFE) << 4;
BigInteger upperOp1 = op1.shiftRight(ndiv2);
BigInteger upperOp2 = op2.shiftRight(ndiv2);
BigInteger lowerOp1 = op1.subtract(upperOp1.shiftLeft(ndiv2));
BigInteger lowerOp2 = op2.subtract(upperOp2.shiftLeft(ndiv2));
BigInteger upper = karatsuba(upperOp1, upperOp2);
BigInteger lower = karatsuba(lowerOp1, lowerOp2);
BigInteger middle = karatsuba( upperOp1.subtract(lowerOp1),
lowerOp2.subtract(upperOp2));
middle = middle.add(upper).add(lower);
middle = middle.shiftLeft(ndiv2);
upper = upper.shiftLeft(ndiv2 << 1);
return upper.add(middle).add(lower);
}
internal static BigInteger add(BigInteger op1, BigInteger op2)
{
int[] resDigits;
int resSign;
int op1Sign = op1.sign;
int op2Sign = op2.sign;
if (op1Sign == 0) {
return op2;
}
if (op2Sign == 0) {
return op1;
}
int op1Len = op1.numberLength;
int op2Len = op2.numberLength;
if (op1Len + op2Len == 2) {
long a = (op1.digits[0] & 0xFFFFFFFFL);
long b = (op2.digits[0] & 0xFFFFFFFFL);
long ress;
int valueLo;
int valueHi;
if (op1Sign == op2Sign) {
ress = a + b;
valueLo = (int) ress;
valueHi = (int) ((long)(((ulong)ress) >> 32));
return ((valueHi == 0) ? new BigInteger(op1Sign, valueLo)
: new BigInteger(op1Sign, 2, new int[] { valueLo,
valueHi }));
}
return BigInteger.valueOf((op1Sign < 0) ? (b - a) : (a - b));
} else if (op1Sign == op2Sign) {
resSign = op1Sign;
// an augend should not be shorter than addend
resDigits = (op1Len >= op2Len) ? add(op1.digits, op1Len,
op2.digits, op2Len) : add(op2.digits, op2Len, op1.digits,
op1Len);
} else { // signs are different
int cmp = ((op1Len != op2Len) ? ((op1Len > op2Len) ? 1 : -1)
: compareArrays(op1.digits, op2.digits, op1Len));
if (cmp == BigInteger.EQUALS) {
return BigInteger.ZERO;
}
// a minuend should not be shorter than subtrahend
if (cmp == BigInteger.GREATER) {
resSign = op1Sign;
resDigits = subtract(op1.digits, op1Len, op2.digits, op2Len);
} else {
resSign = op2Sign;
resDigits = subtract(op2.digits, op2Len, op1.digits, op1Len);
}
}
BigInteger res = new BigInteger(resSign, resDigits.Length, resDigits);
res.cutOffLeadingZeroes();
return res;
}
internal static BigInteger andNegative(BigInteger longer, BigInteger shorter)
{
int iLonger = longer.getFirstNonzeroDigit();
int iShorter = shorter.getFirstNonzeroDigit();
// Does shorter matter?
if (iLonger >= shorter.numberLength) {
return longer;
}
int resLength;
int[] resDigits;
int i = Math.Max(iShorter, iLonger);
int digit;
if (iShorter > iLonger) {
digit = -shorter.digits[i] & ~longer.digits[i];
} else if (iShorter < iLonger) {
digit = ~shorter.digits[i] & -longer.digits[i];
} else {
digit = -shorter.digits[i] & -longer.digits[i];
}
if (digit == 0) {
for (i++; i < shorter.numberLength && (digit = ~(longer.digits[i] | shorter.digits[i])) == 0; i++)
; // digit = ~longer.digits[i] & ~shorter.digits[i]
if (digit == 0) {
// shorter has only the remaining virtual sign bits
for ( ; i < longer.numberLength && (digit = ~longer.digits[i]) == 0; i++)
;
if (digit == 0) {
resLength = longer.numberLength + 1;
resDigits = new int[resLength];
resDigits[resLength - 1] = 1;
return new BigInteger(-1, resLength, resDigits);
}
}
}
resLength = longer.numberLength;
resDigits = new int[resLength];
resDigits[i] = -digit;
for (i++; i < shorter.numberLength; i++){
// resDigits[i] = ~(~longer.digits[i] & ~shorter.digits[i];)
resDigits[i] = longer.digits[i] | shorter.digits[i];
}
// shorter has only the remaining virtual sign bits
for( ; i < longer.numberLength; i++){
resDigits[i] = longer.digits[i];
}
BigInteger result = new BigInteger(-1, resLength, resDigits);
return result;
}
/** @see BigInteger#doubleValue() */
internal static double bigInteger2Double(BigInteger val)
{
// val.bitLength() < 64
if ((val.numberLength < 2)
|| ((val.numberLength == 2) && (val.digits[1] > 0))) {
return val.longValue();
}
// val.bitLength() >= 33 * 32 > 1024
if (val.numberLength > 32) {
return ((val.sign > 0) ? double.PositiveInfinity
: double.NegativeInfinity);
}
return Convert.ToDouble(val.ToString());
}
internal static BigInteger flipBit(BigInteger val, int n)
{
int resSign = (val.sign == 0) ? 1 : val.sign;
int intCount = n >> 5;
int bitN = n & 31;
int resLength = Math.Max(intCount + 1, val.numberLength) + 1;
int[] resDigits = new int[resLength];
int i;
int bitNumber = 1 << bitN;
Array.Copy(val.digits, 0, resDigits, 0, val.numberLength);
if (val.sign < 0) {
if (intCount >= val.numberLength) {
resDigits[intCount] = bitNumber;
} else {
//val.sign<0 y intCount < val.numberLength
int firstNonZeroDigit = val.getFirstNonzeroDigit();
if (intCount > firstNonZeroDigit) {
resDigits[intCount] ^= bitNumber;
} else if (intCount < firstNonZeroDigit) {
resDigits[intCount] = -bitNumber;
for (i=intCount + 1; i < firstNonZeroDigit; i++) {
resDigits[i]=-1;
}
resDigits[i] = resDigits[i]--;
} else {
i = intCount;
resDigits[i] = -((-resDigits[intCount]) ^ bitNumber);
if (resDigits[i] == 0) {
for (i++; resDigits[i] == -1 ; i++) {
resDigits[i] = 0;
}
resDigits[i]++;
}
}
}
} else {//case where val is positive
resDigits[intCount] ^= bitNumber;
}
BigInteger result = new BigInteger(resSign, resLength, resDigits);
result.cutOffLeadingZeroes();
return result;
}
internal static int bitLength(BigInteger val)
{
if (val.sign == 0) {
return 0;
}
int bLength = (val.numberLength << 5);
int highDigit = val.digits[val.numberLength - 1];
if (val.sign < 0) {
int i = val.getFirstNonzeroDigit();
// We reduce the problem to the positive case.
if (i == val.numberLength - 1) {
highDigit--;
}
}
// Subtracting all sign bits
bLength -= BigDecimal.numberOfLeadingZeros(highDigit);
return bLength;
}
internal static int bitCount(BigInteger val)
{
int bCount = 0;
if (val.sign == 0) {
return 0;
}
int i = val.getFirstNonzeroDigit();;
if (val.sign > 0) {
for ( ; i < val.numberLength; i++) {
bCount += BigDecimal.bitCount(val.digits[i]);
}
} else {// (sign < 0)
// this digit absorbs the carry
bCount += BigDecimal.bitCount(-val.digits[i]);
for (i++; i < val.numberLength; i++) {
bCount += BigDecimal.bitCount(~val.digits[i]);
}
// We take the complement sum:
bCount = (val.numberLength << 5) - bCount;
}
return bCount;
}
internal static BigInteger nextProbablePrime(BigInteger n)
{
// PRE: n >= 0
int i, j;
int certainty;
int gapSize = 1024; // for searching of the next probable prime number
int[] modules = new int[primes.Length];
bool[] isDivisible = new bool[gapSize];
BigInteger startPoint;
BigInteger probPrime;
// If n < "last prime of table" searches next prime in the table
if ((n.numberLength == 1) && (n.digits[0] >= 0)
&& (n.digits[0] < primes[primes.Length - 1])) {
for (i = 0; n.digits[0] >= primes[i]; i++) {
;
}
return BIprimes[i];
}
/*
* Creates a "N" enough big to hold the next probable prime Note that: N <
* "next prime" < 2*N
*/
startPoint = new BigInteger(1, n.numberLength,
new int[n.numberLength + 1]);
Array.Copy(n.digits, startPoint.digits, n.numberLength);
// To fix N to the "next odd number"
if (n.testBit(0)) {
Elementary.inplaceAdd(startPoint, 2);
} else {
startPoint.digits[0] |= 1;
}
// To set the improved certainly of Miller-Rabin
j = startPoint.bitLength();
for (certainty = 2; j < BITS[certainty]; certainty++) {
;
}
// To calculate modules: N mod p1, N mod p2, ... for first primes.
for (i = 0; i < primes.Length; i++) {
modules[i] = Division.remainder(startPoint, primes[i]) - gapSize;
}
while (true) {
// At this point, all numbers in the gap are initialized as
// probably primes
Array.Clear(isDivisible, 0, isDivisible.Length);
// To discard multiples of first primes
for (i = 0; i < primes.Length; i++) {
modules[i] = (modules[i] + gapSize) % primes[i];
j = (modules[i] == 0) ? 0 : (primes[i] - modules[i]);
for (; j < gapSize; j += primes[i]) {
isDivisible[j] = true;
}
}
// To execute Miller-Rabin for non-divisible numbers by all first
// primes
for (j = 0; j < gapSize; j++) {
if (!isDivisible[j]) {
probPrime = startPoint.copy();
Elementary.inplaceAdd(probPrime, j);
if (millerRabin(probPrime, certainty)) {
return probPrime;
}
}
}
Elementary.inplaceAdd(startPoint, gapSize);
}
}
private static void setFromString(BigInteger bi, String val, int radix)
{
int sign;
int[] digits;
int numberLength;
int stringLength = val.Length;
int startChar;
int endChar = stringLength;
if (val[0] == '-') {
sign = -1;
startChar = 1;
stringLength--;
} else {
sign = 1;
startChar = 0;
}
/*
* We use the following algorithm: split a string into portions of n
* characters and convert each portion to an integer according to the
* radix. Then convert an exp(radix, n) based number to binary using the
* multiplication method. See D. Knuth, The Art of Computer Programming,
* vol. 2.
*/
int charsPerInt = Conversion.digitFitInInt[radix];
int bigRadixDigitsLength = stringLength / charsPerInt;
int topChars = stringLength % charsPerInt;
if (topChars != 0) {
bigRadixDigitsLength++;
}
digits = new int[bigRadixDigitsLength];
// Get the maximal power of radix that fits in int
int bigRadix = Conversion.bigRadices[radix - 2];
// Parse an input string and accumulate the BigInteger's magnitude
int digitIndex = 0; // index of digits array
int substrEnd = startChar + ((topChars == 0) ? charsPerInt : topChars);
int newDigit;
for (int substrStart = startChar; substrStart < endChar; substrStart = substrEnd, substrEnd = substrStart
+ charsPerInt) {
int bigRadixDigit = Convert.ToInt32(val.Substring(substrStart,
substrEnd - substrStart), radix);
newDigit = Multiplication.multiplyByInt(digits, digitIndex,
bigRadix);
newDigit += Elementary
.inplaceAdd(digits, digitIndex, bigRadixDigit);
digits[digitIndex++] = newDigit;
}
numberLength = digitIndex;
bi.sign = sign;
bi.numberLength = numberLength;
bi.digits = digits;
bi.cutOffLeadingZeroes();
}
public BigInteger xor(BigInteger val)
{
return Logical.xor(this, val);
}
public BigInteger subtract(BigInteger val)
{
return Elementary.subtract(this, val);
}
public BigInteger remainder(BigInteger divisor)
{
if (divisor.sign == 0) {
throw new ArithmeticException("BigInteger divide by zero");
}
int thisLen = numberLength;
int divisorLen = divisor.numberLength;
if (((thisLen != divisorLen) ? ((thisLen > divisorLen) ? 1 : -1)
: Elementary.compareArrays(digits, divisor.digits, thisLen)) == LESS) {
return this;
}
int resLength = divisorLen;
int[] resDigits = new int[resLength];
if (resLength == 1) {
resDigits[0] = Division.remainderArrayByInt(digits, thisLen,
divisor.digits[0]);
} else {
int qLen = thisLen - divisorLen + 1;
resDigits = Division.divide(null, qLen, digits, thisLen,
divisor.digits, divisorLen);
}
BigInteger result = new BigInteger(sign, resLength, resDigits);
result.cutOffLeadingZeroes();
return result;
}
public BigInteger multiply(BigInteger val)
{
// This let us to throw NullReferenceException when val == null
if (val.sign == 0) {
return ZERO;
}
if (sign == 0) {
return ZERO;
}
return Multiplication.multiply(this, val);
}
public int compareTo(BigInteger val)
{
if (sign > val.sign) {
return GREATER;
}
if (sign < val.sign) {
return LESS;
}
if (numberLength > val.numberLength) {
return sign;
}
if (numberLength < val.numberLength) {
return -val.sign;
}
// Equal sign and equal numberLength
return (sign * Elementary.compareArrays(digits, val.digits,
numberLength));
}
public BigInteger modInverse(BigInteger m)
{
if (m.sign <= 0) {
throw new ArithmeticException("BigInteger: modulus not positive");
}
// If both are even, no inverse exists
if (!(testBit(0) || m.testBit(0))) {
throw new ArithmeticException("BigInteger not invertible.");
}
if (m.isOne()) {
return ZERO;
}
// From now on: (m > 1)
BigInteger res = Division.modInverseMontgomery(abs().mod(m), m);
if (res.sign == 0) {
throw new ArithmeticException("BigInteger not invertible.");
}
res = ((sign < 0) ? m.subtract(res) : res);
return res;
}
public BigInteger gcd(BigInteger val)
{
BigInteger val1 = this.abs();
BigInteger val2 = val.abs();
// To avoid a possible division by zero
if (val1.signum() == 0) {
return val2;
} else if (val2.signum() == 0) {
return val1;
}
// Optimization for small operands
// (op2.bitLength() < 64) and (op1.bitLength() < 64)
if (((val1.numberLength == 1) || ((val1.numberLength == 2) && (val1.digits[1] > 0)))
&& (val2.numberLength == 1 || (val2.numberLength == 2 && val2.digits[1] > 0))) {
return BigInteger.valueOf(Division.gcdBinary(val1.longValue(), val2
.longValue()));
}
return Division.gcdBinary(val1.copy(), val2.copy());
}
public BigInteger[] divideAndRemainder(BigInteger divisor)
{
int divisorSign = divisor.sign;
if (divisorSign == 0) {
throw new ArithmeticException("BigInteger divide by zero");
}
int divisorLen = divisor.numberLength;
int[] divisorDigits = divisor.digits;
if (divisorLen == 1) {
return Division.divideAndRemainderByInteger(this, divisorDigits[0],
divisorSign);
}
// res[0] is a quotient and res[1] is a remainder:
int[] thisDigits = digits;
int thisLen = numberLength;
int cmp = (thisLen != divisorLen) ? ((thisLen > divisorLen) ? 1 : -1)
: Elementary.compareArrays(thisDigits, divisorDigits, thisLen);
if (cmp < 0) {
return new BigInteger[] { ZERO, this };
}
int thisSign = sign;
int quotientLength = thisLen - divisorLen + 1;
int remainderLength = divisorLen;
int quotientSign = ((thisSign == divisorSign) ? 1 : -1);
int[] quotientDigits = new int[quotientLength];
int[] remainderDigits = Division.divide(quotientDigits, quotientLength,
thisDigits, thisLen, divisorDigits, divisorLen);
BigInteger result0 = new BigInteger(quotientSign, quotientLength,
quotientDigits);
BigInteger result1 = new BigInteger(thisSign, remainderLength,
remainderDigits);
result0.cutOffLeadingZeroes();
result1.cutOffLeadingZeroes();
return new BigInteger[] { result0, result1 };
}
public BigInteger divide(BigInteger divisor)
{
if (divisor.sign == 0) {
throw new ArithmeticException("BigInteger divide by zero");
}
int divisorSign = divisor.sign;
if (divisor.isOne()) {
return ((divisor.sign > 0) ? this : this.negate());
}
int thisSign = sign;
int thisLen = numberLength;
int divisorLen = divisor.numberLength;
if (thisLen + divisorLen == 2) {
long val = (digits[0] & 0xFFFFFFFFL)
/ (divisor.digits[0] & 0xFFFFFFFFL);
if (thisSign != divisorSign) {
val = -val;
}
return valueOf(val);
}
int cmp = ((thisLen != divisorLen) ? ((thisLen > divisorLen) ? 1 : -1)
: Elementary.compareArrays(digits, divisor.digits, thisLen));
if (cmp == EQUALS) {
return ((thisSign == divisorSign) ? ONE : MINUS_ONE);
}
if (cmp == LESS) {
return ZERO;
}
int resLength = thisLen - divisorLen + 1;
int[] resDigits = new int[resLength];
int resSign = ((thisSign == divisorSign) ? 1 : -1);
if (divisorLen == 1) {
Division.divideArrayByInt(resDigits, digits, thisLen,
divisor.digits[0]);
} else {
Division.divide(resDigits, resLength, digits, thisLen,
divisor.digits, divisorLen);
}
BigInteger result = new BigInteger(resSign, resLength, resDigits);
result.cutOffLeadingZeroes();
return result;
}
private static bool millerRabin(BigInteger n, int t)
{
// PRE: n >= 0, t >= 0
BigInteger x; // x := UNIFORM{2...n-1}
BigInteger y; // y := x^(q * 2^j) mod n
BigInteger n_minus_1 = n.subtract(BigInteger.ONE); // n-1
int bitLength = n_minus_1.bitLength(); // ~ log2(n-1)
// (q,k) such that: n-1 = q * 2^k and q is odd
int k = n_minus_1.getLowestSetBit();
BigInteger q = n_minus_1.shiftRight(k);
Random rnd = new Random();
for (int i = 0; i < t; i++) {
// To generate a witness 'x', first it use the primes of table
if (i < primes.Length) {
x = BIprimes[i];
} else {/*
* It generates random witness only if it's necesssary. Note
* that all methods would call Miller-Rabin with t <= 50 so
* this part is only to do more robust the algorithm
*/
do {
x = new BigInteger(bitLength, rnd);
} while ((x.compareTo(n) >= BigInteger.EQUALS) || (x.sign == 0)
|| x.isOne());
}
y = x.modPow(q, n);
if (y.isOne() || y.Equals(n_minus_1)) {
continue;
}
for (int j = 1; j < k; j++) {
if (y.Equals(n_minus_1)) {
continue;
}
y = y.multiply(y).mod(n);
if (y.isOne()) {
return false;
}
}
if (!y.Equals(n_minus_1)) {
return false;
}
}
return true;
}
public BigInteger modPow(BigInteger exponent, BigInteger m)
{
if (m.sign <= 0) {
throw new ArithmeticException("BigInteger: modulus not positive");
}
BigInteger _base = this;
if (m.isOne() | (exponent.sign > 0 & _base.sign == 0)) {
return BigInteger.ZERO;
}
if (_base.sign == 0 && exponent.sign == 0) {
return BigInteger.ONE;
}
if (exponent.sign < 0) {
_base = modInverse(m);
exponent = exponent.negate();
}
// From now on: (m > 0) and (exponent >= 0)
BigInteger res = (m.testBit(0)) ? Division.oddModPow(_base.abs(),
exponent, m) : Division.evenModPow(_base.abs(), exponent, m);
if ((_base.sign < 0) && exponent.testBit(0)) {
// -b^e mod m == ((-1 mod m) * (b^e mod m)) mod m
res = m.subtract(BigInteger.ONE).multiply(res).mod(m);
}
// else exponent is even, so base^exp is positive
return res;
}
public BigInteger max(BigInteger val)
{
return ((this.compareTo(val) == GREATER) ? this : val);
}
public BigInteger andNot(BigInteger val)
{
return Logical.andNot(this, val);
}
internal static String toDecimalScaledString(BigInteger val, int scale)
{
int sign = val.sign;
int numberLength = val.numberLength;
int[] digits = val.digits;
int resLengthInChars;
int currentChar;
char[] result;
if (sign == 0) {
switch (scale) {
case 0:
return "0"; //$NON-NLS-1$
case 1:
return "0.0"; //$NON-NLS-1$
case 2:
return "0.00"; //$NON-NLS-1$
case 3:
return "0.000"; //$NON-NLS-1$
case 4:
return "0.0000"; //$NON-NLS-1$
case 5:
return "0.00000"; //$NON-NLS-1$
case 6:
return "0.000000"; //$NON-NLS-1$
default:
StringBuilder result1x = new StringBuilder();
if (scale < 0) {
result1x.Append("0E+"); //$NON-NLS-1$
} else {
result1x.Append("0E"); //$NON-NLS-1$
}
result1x.Append(-scale);
return result1x.ToString();
}
}
// one 32-bit unsigned value may contains 10 decimal digits
resLengthInChars = numberLength * 10 + 1 + 7;
// Explanation why +1+7:
// +1 - one char for sign if needed.
// +7 - For "special case 2" (see below) we have 7 free chars for
// inserting necessary scaled digits.
result = new char[resLengthInChars + 1];
// allocated [resLengthInChars+1] characters.
// a free latest character may be used for "special case 1" (see
// below)
currentChar = resLengthInChars;
if (numberLength == 1) {
int highDigit = digits[0];
if (highDigit < 0) {
long v = highDigit & 0xFFFFFFFFL;
do {
long prev = v;
v /= 10;
result[--currentChar] = (char) (0x0030 + ((int) (prev - v * 10)));
} while (v != 0);
} else {
int v = highDigit;
do {
int prev = v;
v /= 10;
result[--currentChar] = (char) (0x0030 + (prev - v * 10));
} while (v != 0);
}
} else {
int[] temp = new int[numberLength];
int tempLen = numberLength;
Array.Copy(digits, temp, tempLen);
while (true) {
// divide the array of digits by bigRadix and convert
// remainders
// to characters collecting them in the char array
long result11 = 0;
for (int i1 = tempLen - 1; i1 >= 0; i1--) {
long temp1 = (result11 << 32)
+ (temp[i1] & 0xFFFFFFFFL);
long res = divideLongByBillion(temp1);
temp[i1] = (int) res;
result11 = (int) (res >> 32);
}
int resDigit = (int) result11;
int previous = currentChar;
do {
result[--currentChar] = (char) (0x0030 + (resDigit % 10));
} while (((resDigit /= 10) != 0) && (currentChar != 0));
int delta = 9 - previous + currentChar;
for (int i = 0; (i < delta) && (currentChar > 0); i++) {
result[--currentChar] = '0';
}
int j = tempLen - 1;
bool bigloop = false;
for (; temp[j] == 0; j--) {
if (j == 0) { // means temp[0] == 0
bigloop = true;
break;
}
}
if(bigloop) break;
tempLen = j + 1;
}
while (result[currentChar] == '0') {
currentChar++;
}
}
bool negNumber = (sign < 0);
int exponent = resLengthInChars - currentChar - scale - 1;
if (scale == 0) {
if (negNumber) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars
- currentChar);
}
if ((scale > 0) && (exponent >= -6)) {
if (exponent >= 0) {
// special case 1
int insertPoint = currentChar + exponent;
for (int j = resLengthInChars - 1; j >= insertPoint; j--) {
result[j + 1] = result[j];
}
result[++insertPoint] = '.';
if (negNumber) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars
- currentChar + 1);
}
// special case 2
for (int j = 2; j < -exponent + 1; j++) {
result[--currentChar] = '0';
}
result[--currentChar] = '.';
result[--currentChar] = '0';
if (negNumber) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars
- currentChar);
}
int startPoint = currentChar + 1;
int endPoint = resLengthInChars;
StringBuilder result1 = new StringBuilder(16 + endPoint - startPoint);
if (negNumber) {
result1.Append('-');
}
if (endPoint - startPoint >= 1) {
result1.Append(result[currentChar]);
result1.Append('.');
result1.Append(result, currentChar + 1, resLengthInChars
- currentChar - 1);
} else {
result1.Append(result, currentChar, resLengthInChars
- currentChar);
}
result1.Append('E');
if (exponent > 0) {
result1.Append('+');
}
result1.Append(exponent.ToString());
return result1.ToString();
}
public BigInteger min(BigInteger val)
{
return ((this.compareTo(val) == LESS) ? this : val);
}
internal static String bigInteger2String(BigInteger val, int radix)
{
int sign = val.sign;
int numberLength = val.numberLength;
int[] digits = val.digits;
if (sign == 0) {
return "0"; //$NON-NLS-1$
}
if (numberLength == 1) {
int highDigit = digits[numberLength - 1];
long v = highDigit & 0xFFFFFFFFL;
if (sign < 0) {
v = -v;
}
return Convert.ToString(v, radix);
}
if ((radix == 10) || (radix < 0)
|| (radix > 26)) {
return val.ToString();
}
double bitsForRadixDigit;
bitsForRadixDigit = Math.Log(radix) / Math.Log(2);
int resLengthInChars = (int) (val.abs().bitLength() / bitsForRadixDigit + ((sign < 0) ? 1
: 0)) + 1;
char[] result = new char[resLengthInChars];
int currentChar = resLengthInChars;
int resDigit;
if (radix != 16) {
int[] temp = new int[numberLength];
Array.Copy(digits, 0, temp, 0, numberLength);
int tempLen = numberLength;
int charsPerInt = digitFitInInt[radix];
int i;
// get the maximal power of radix that fits in int
int bigRadix = bigRadices[radix - 2];
while (true) {
// divide the array of digits by bigRadix and convert remainders
// to characters collecting them in the char array
resDigit = Division.divideArrayByInt(temp, temp, tempLen,
bigRadix);
int previous = currentChar;
do {
result[--currentChar] = Convert.ToString(resDigit % radix, radix)[0];
} while (((resDigit /= radix) != 0) && (currentChar != 0));
int delta = charsPerInt - previous + currentChar;
for (i = 0; i < delta && currentChar > 0; i++) {
result[--currentChar] = '0';
}
for (i = tempLen - 1; (i > 0) && (temp[i] == 0); i--) {
;
}
tempLen = i + 1;
if ((tempLen == 1) && (temp[0] == 0)) { // the quotient is 0
break;
}
}
} else {
// radix == 16
for (int i = 0; i < numberLength; i++) {
for (int j = 0; (j < 8) && (currentChar > 0); j++) {
resDigit = digits[i] >> (j << 2) & 0xf;
result[--currentChar] = Convert.ToString(resDigit % radix, 16)[0];
}
}
}
while (result[currentChar] == '0') {
currentChar++;
}
if (sign == -1) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars - currentChar);
}
public BigInteger mod(BigInteger m)
{
if (m.sign <= 0) {
throw new ArithmeticException("BigInteger: modulus not positive");
}
BigInteger rem = remainder(m);
return ((rem.sign < 0) ? rem.add(m) : rem);
}